Solve for $x$ and $y$ using elimination. ${-x-3y = -24}$ ${x+2y = 17}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-x-3y = -24}\thinspace$ to find $x$ ${-x - 3}{(7)}{= -24}$ $-x-21 = -24$ $-x-21{+21} = -24{+21}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 7}$ into $\thinspace {x+2y = 17}\thinspace$ and get the same answer for $x$ : ${x + 2}{(7)}{= 17}$ ${x = 3}$